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Proceedings ArticleDOI

A polytopic approach for the nonlinear unknown input functional observers design: Application to a quadrotor aerial robots landing

TL;DR: The proposed approach consists in rewriting the nonlinear model in a polytopic form applying the Sector Non-linearity Transformation (SNT) and then applying the proposed algorithm for the observer design.
Abstract: This paper considers a method of designing functional observers for continuous time nonlinear systems subject to unknown inputs. The proposed approach consists in rewriting the nonlinear model in a polytopic form (also known as multiple or Takagi-Sugeno models) applying the Sector Non-linearity Transformation (SNT) and then apply the proposed algorithm for the observer design. Sufficient conditions for the asymptotic stability of the estimation error are given in terms of linear matrix inequalities (LMls) and rank conditions. An application to a quadrotor aerial robots landing is then presented.

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Summary

  • This paper considers a method of designing functional observers for continuous time nonlinear systems subject to unknown inputs.
  • The proposed approach consists in rewriting the nonlinear model in a polytopic form (also known as multiple or Takagi-Sugeno models) applying the Sector Nonlinearity Transformation (SNT) and then apply the proposed algorithm for the observer design.
  • Sufficient conditions for the asymptotic stability of the estimation error are given in terms of linear matrix inequalities (LMIs) and rank conditions.

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A Polytopic Approach for the Nonlinear Unknown Input Functional
Observers Design: Application to a Quadrotor Aerial Robots Landing
Souad Bezzaoucha
1
, Holger Voos
1
and Mohamed Darouach
2
Abstract This paper considers a method of designing func-
tional observers for continuous time nonlinear systems subject
to unknown inputs. The proposed approach consists in re-
writing the nonlinear model in a polytopic form (also known
as multiple or Takagi-Sugeno models) applying the Sector Non-
linearity Transformation (SNT) and then apply the proposed
algorithm for the observer design. Sufficient conditions for the
asymptotic stability of the estimation error are given in terms
of linear matrix inequalities (LMIs) and rank conditions.
An application to a quadrotor aerial robots landing is then
presented.
1
Souad Bezzaoucha and Holger Voos are with the Interdisciplinary
Centre for Security, Reliability and Trust (SnT), Automatic Control
Research Group, University of Luxembourg, Campus Kirchberg, 6
rue Coudenhove-Kalergi L-1359, Luxembourg souad.bezzaoucha,
holger.voos@uni.lu
2
Mohamed Darouach is with the Research Center for Auto-
matic Control of Nancy (CRAN), Universit
´
e de Lorraine, IUT de
Longwy, 186 rue de Lorraine, 54400 Cosnes et Romain, France
mohamed.darouach@univ-lorraine.fr
References
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Journal ArticleDOI
TL;DR: The discrete-time uncertain nonlinear models are considered in a Takagi-Sugeno form and their stabilization is studied through a non- quadratic Lyapunov function and the results are shown to always include the classical cases.
Abstract: The discrete-time uncertain nonlinear models are considered in a Takagi-Sugeno form and their stabilization is studied through a non- quadratic Lyapunov function. The classical conditions consider a one- sample variation, here, the main results are obtained considering k samples variation, i.e., Deltak V(x(t)) = V(x(t + k)) - V(x(t)). The results are shown to always include the classical cases, and several examples illustrate the effectiveness of the approach.

331 citations


"A polytopic approach for the nonlin..." refers methods in this paper

  • ...Thanks to the convexity of the weighting functions and to the linearity of the subsystems defining the vertices, some results can be established for nonlinear systems [7], [12], [17] using tools borrowed from the linear theory [18], [9]....

    [...]

Journal ArticleDOI
TL;DR: Control law design with an observer for models in the Takagi-Sugeno's (TS) form in the general case where the nonlinearities and the variables involved are not measurable is dealt with.

285 citations


"A polytopic approach for the nonlin..." refers methods in this paper

  • ...Thanks to the convexity of the weighting functions and to the linearity of the subsystems defining the vertices, some results can be established for nonlinear systems [7], [12], [17] using tools borrowed from the linear theory [18], [9]....

    [...]

Journal ArticleDOI
TL;DR: An observer design is presented which makes use of bounds on the slope of system nonlinearities to ensure global asymptotic stability and one such certainty-equivalence design is illustrated on an active magnetic bearing example.
Abstract: An observer design is presented which makes use of bounds on the slope of system nonlinearities. Necessary and sufficient conditions are derived for the feasibility of the design. A class of state feedback control laws are characterized which, when implemented with the observer states, ensure global asymptotic stability. One such certainty-equivalence design is illustrated on an active magnetic bearing example.

273 citations


"A polytopic approach for the nonlin..." refers background in this paper

  • ...Observer design theory for nonlinear systems has been widely considered in the last decade and several contributions and theoretical approaches can be found in the literature (see for example [1], [11], [13], [16], [15])....

    [...]

Journal ArticleDOI
01 Feb 2002
TL;DR: The main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches and consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.
Abstract: We focus on the analysis and design of two different sliding mode observers for dynamic Takagi-Sugeno (TS) fuzzy systems. A nonlinear system of this class is composed of multiple affine local linear models that are smoothly interpolated by weighting functions resulting from a fuzzy partitioning of the state space of a given nonlinear system subject to observation. The Takagi-Sugeno fuzzy system is then an accurate approximation of the original nonlinear system. Our approach to the analysis and design of observers for Takagi-Sugeno fuzzy systems is based on extending sliding mode observer schemes to the case of interpolated multiple local affine linear models. Thus, our main contribution is nonlinear observer analysis and design methods that can effectively deal with model/plant mismatches. Furthermore, we consider the difficult case when the weighting functions in the Takagi-Sugeno fuzzy system depend on the estimated state.

265 citations


"A polytopic approach for the nonlin..." refers background in this paper

  • ...) acts like an unstructured vanishing perturbation assumed to be bounded (see [ [2]], [ [6]] and references therein) and its effect can be minimized....

    [...]

Journal ArticleDOI
TL;DR: This paper presents straightforward derivations of the functional observers design for linear time-invariant multivariable systems where the order of these observers is equal to the dimension of the vector to be estimated.
Abstract: This paper presents straightforward derivations of the functional observers design for linear time-invariant multivariable systems. The order of these observers is equal to the dimension /spl tau/ of the vector to be estimated. Necessary and sufficient conditions for the existence and stability of these observers are given. Illustrative examples are included.

226 citations


"A polytopic approach for the nonlin..." refers background in this paper

  • ...Most of the works devoted to these observers are for linear systems where necessary and sufficient conditions for their existence were given (see [8], [26], [19], [10] and [20])....

    [...]